A cyclist must lean into a turn to prevent tipping over in the other direction. To see why this is so, consider the sketches below. The sketch on the left represents a cyclist, seen from behind, who is attempting to remain upright while turning to the left. There are three forces acting on the rider and bicycle.
The weight of the rider and bicycle, W, acts vertically downward from their center of gravity. The normal force, N, of the road acts vertically upward from a point below the center of gravity. And the frictional force, F, of the road acts horizontally to the left. Turning on a bike requires a net force called centripetal force. The frictional force provides the centripetal force necessary to turn the cyclist to the left. But the frictional force also produces a clockwise torque that will cause the rider and bicycle to tip clockwise to the right. In the sketch on the right the cyclist is leaning in the direction of turn. Now the normal force of the road does not act through the center of gravity. It produces a counterclockwise torque that cancels out the clockwise torque of the frictional force. Thus there is no tendency for the cyclist to tip to the right.
Another way to look this is to recall Newton’s 1st law of motion: an object in motion will continue moving in a straight line until acted on by an outside force. The bicyclist rides in a straight line until he or she decides to steer the bike in the direction of the turn. The steering merely rotates the bike but the bicyclist and the bike will keep moving in the same direction according to Newton’s law. However since the wheels are now pointing in a different direction, the friction of the road will cause the bike to tumble over. Thus to counter act the tumbling, the bicyclist must lean in the other direction which is into the turn.
When a car or truck makes a turn it cannot lean into the turn. The torque that prevents it from tipping away from the turn arises from the normal force on the outside tires being larger than the normal force on the inside tires. However, a truck with a high center of gravity can tip over if it attempts to make the turn too fast. At turns on high speed roads there will often be a sign warning truck drivers of this.
Answered By: Kenneth S. Mendelson, Marquette University